class

CubeRootBackward

CubeRootBackward

source edit

Autograd node for element-wise cube root: $y = \sqrt[3]{x} = x^{1/3}$ .

Unlike sqrt, cube root is real-valued for all real inputs — negative arguments produce negative outputs and the operation is monotone increasing. The backward formula divides by $3 y^{2}$ , which is the only undefined point (at $x = y = 0$ ).

Math

Forward

$y_i = \sqrt[3]{x_i} = \operatorname{sgn}(x_i)\, |x_i|^{1/3}$

Backward

\frac{\partial L}{\partial y_i}$$ **See Also** `cube_root_op`.

Attributes

kSavesInputbool

false — the input is not needed for the backward pass.

kSavesOutputbool

true — the forward output

y

is saved so the backward pass can compute

1 / (3 y^{2})

without re-invoking the cube-root kernel.

schema_v1OpSchema

Op name "cube_root" with AmpPolicy::ForceFP32 because the cube root is numerically unreliable in half precision (loss of accuracy near zero and for very large magnitudes).

Notes

CPU dispatch uses Apple Accelerate's vvcbrtf (vector cube root in float32); GPU dispatch routes through MLX's power primitive applied with exponent $1/3$ . The gradient diverges at $x = 0$ — callers should guard against zero inputs if they intend to backpropagate.

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::cube_root to compute $y = \sqrt[3]{x}$ .

Methods

grad_formula

→Storage

int grad_formula(const int & g)

source edit

Computes $\partial L/\partial x = g / (3 y^{2})$ from the saved output $y$ — squaring $y$ is cheaper than recomputing $\sqrt[3]{x}^{2}$ .

Parameters

gconst Storage&

Upstream gradient

\partial L/\partial y

Returns

Storage

Gradient with respect to x. Undefined at slots where the saved output is zero (division by zero); callers must avoid differentiating through $x = 0$ .

class

CubeRootBackward

CubeRootBackward

source edit

Autograd node for element-wise cube root: $y = \sqrt[3]{x} = x^{1/3}$ .

Math

Forward

$y_i = \sqrt[3]{x_i} = \operatorname{sgn}(x_i)\, |x_i|^{1/3}$

Backward

\frac{\partial L}{\partial y_i}$$ **See Also** `cube_root_op`.

Attributes

kSavesInputbool

false — the input is not needed for the backward pass.

kSavesOutputbool

true — the forward output

y

is saved so the backward pass can compute

1 / (3 y^{2})

without re-invoking the cube-root kernel.

schema_v1OpSchema

Op name "cube_root" with AmpPolicy::ForceFP32 because the cube root is numerically unreliable in half precision (loss of accuracy near zero and for very large magnitudes).

Notes

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::cube_root to compute $y = \sqrt[3]{x}$ .

Methods

grad_formula

→Storage

int grad_formula(const int & g)

source edit

Computes $\partial L/\partial x = g / (3 y^{2})$ from the saved output $y$ — squaring $y$ is cheaper than recomputing $\sqrt[3]{x}^{2}$ .

Parameters

gconst Storage&

Upstream gradient

\partial L/\partial y

Returns

Storage

Gradient with respect to x. Undefined at slots where the saved output is zero (division by zero); callers must avoid differentiating through $x = 0$ .